The naming of the tutorial as "Kingdom" is a bit confusing for new players. But once you are in it, the fact that it is a tutorial is pretty evident with the narrator guiding you with each step that must be completed before the next step is presented to you.

It is also confusing for some people that the game doesn't automatically pass you from the Kingdom to the Republic or the Republic to the Empire campaigns. Once you complete the last cities in each campaign you have to return to the main menu where the next campaign will then be unlocked and playable.

The only people that seem to have a problem with the Kingdom level are those that don't bother to listen to the narrator guide and do the step that is being called for. People end up waiting for something to happen that won't occur because a called for step was missed.

Once you get the invasion of the barbarians and you have defeated them the scenario will officially end and end the tutorial. The barbarian invasion won't occur unless the steps called for are followed. Of course, if you overbuild your city too fast and go into debt long enough, your favor rating with Caesar will fall to a point where he will dispatch his legions to remove you from office and you'll get a different kind of "invasion".

As long as the mission summary says "Success" you are done with Brundisium. You can then leave and return to the main menu or keep playing the city for as long as you wish.